Chopping, Channeling, & Sectioning are terms associated with car customizations for hot-rods.
CHOPPING
To chop a roof the pillars and windows are cut down, lowering the overall roofline. "Chopping the top" goes back to the early days of hot rodding in an attempt to reduce the frontal profile of a car and increase its speed potential. Some racers on the dry lakes chopped the tops of their cars so severely that the windows were only a few inches tall. These were sometimes referred to as "mail slot" windows. This sort of bodywork is also popular on custom cars, kustoms, and leadsleds. Roof chopping also quickly became very popular with drag racers for much the same reasons as it did for lakes racers. The first roof chopper is considered to be Sam Barris (see article about his brother) who chopped and customised his brand new 1949 Mercury.
Concept cars often undergo a lowering of their roofs even if the vehicles are based on production models. Automakers use the chopping technique to make them look more "racy", although it would be impractical for normal use.
CHANNELING
To Channel a car the body is also lowered over the frame by removing the floor & refastening it higher inside the body, causing the body to rest closer to the ground without altering the suspension. The overall effect is to give the car body a more massive appearance. Each automobile would have its own engineering challenges as far as modifying the various components of the chassis. Local laws may prevent making the modifications too extreme, and safety would dictate some restraint.
SECTIONING
A related process to channeling a car (and one that has almost the same aim) is Sectioning. Sectioning is the act of removing a horizontal section from the body of a car, lowering the top half onto the bottom half and welding the result back together. The purpose is to reduce the overall height of the bodywork of the car. This sort of bodywork is popular on minitrucks, custom cars, kustoms, and leadsleds.